Theorem 5.1  ([1]})
Let \(p, p^\prime \in \mathbb {N}\)  be coprime. Let \(\Lambda ^{(+)},\Lambda ^{(-)}\)  be dominant weights of \({sl}_{n+1}.Then there exists an irreducible representation of \) Wn+1\( whosecentral charge is\begin{equation}c=n-n(n+1)(n+2) \tfrac{( p^\prime -p)^2}{p p^\prime }\end{equation}and whose conformal dimension \) h\( is given by\begin{equation}c-24h=n - 12 \,\left|\alpha _+ (\Lambda ^{(+)} + \rho ) + \alpha _- (\Lambda ^{(-)} + \rho )\right|^2,\end{equation}where \)\( is as in Theorem \ref {qqpi}, and\) + =  p/p, - = -p/ p\(.\)
